$A$ sample of air contains $N_2$ and $O_2$ saturated with water vapor,with a total pressure of $640 \ torr$. If the water vapor pressure is $40 \ torr$ and the molar ratio of $N_2$ to $O_2$ is $3 : 1$,what is the partial pressure of $N_2$ in the sample in $torr$?

$A$ closed container contains a mixture of non-reacting gases $A$ and $B$. The partial pressures of $A$ and $B$ are $4.5 \ bar$ and $5.5 \ bar$ respectively. Find the mole fractions of $A$ and $B$ respectively.

According to Graham's law of diffusion at a given temperature,the ratio of the rate of diffusion $r_A/r_B$ for gases $A$ and $B$ is given by:

Fill in the blanks:
$(1)$ The properties of gases were first measured by ......... .
$(2)$ The dipole-dipole interaction energy between stationary polar molecules is proportional to .......... .
$(3)$ The interaction energy between rotating polar molecules is proportional to .......... .
$(4)$ The bond energy of a hydrogen bond is about ......... $kJ \ mol^{-1}$.

Show the relationship between different units of pressure.

Internal energy of an ideal gas depends on